Math Snap

STEP 1

Assumptions1. We have a system of two linear equations with three unknowns $x1$, $x$, and $x3$.
. The first equation is $9x1 + x -3x3 =8$.
3. The second equation is $10x +4x3 =0$.

STEP 2

We can write the system of equations as a vector equation by expressing the left-hand side of each equation as a linear combination of vectors, and the right-hand side as a vector.The vector equation can be written as$$x1 \begin{bmatrix}9 \\0 \end{bmatrix} + x2 \begin{bmatrix}1 \\10 \end{bmatrix} + x \begin{bmatrix} - \\4 \end{bmatrix} = \begin{bmatrix}8 \\0 \end{bmatrix}$$This corresponds to choice C in the problem.

We can also write the system of equations as a matrix equation. In a matrix equation, the coefficients of the variables form a matrix, the variables themselves form a column vector, and the constants on the right-hand side of the equations form another column vector.
The matrix equation can be written as$$\begin{bmatrix}9 &1 & -3 \\0 &10 & \end{bmatrix} \begin{bmatrix} x1 \\ x2 \\ x3 \end{bmatrix} = \begin{bmatrix}8 \\0 \end{bmatrix}$$This corresponds to choice B in the problem.